"Quantum Computing" is among those terms that are widely discussed but often poorly understood. The reasons of this state of affairs may be numerous, but possibly the most significant among them is that it is a relatively new scientific area, and it's clear interpretations are not yet widely spread. The main obstacle here is the word "quantum", which refers to quantum mechanics - one of the most counter-intuitive ways to describe our world.
But fear not! This is not a course on quantum mechanics. We will gently touch it in the beginning and then leave it apart, concentrating on the mathematical model of quantum computer, generously developed for us by physicists. This doesn't mean that the whole course is mathematics either (however there will be enough of it). We will build a simple working quantum computer with our bare hands, and we will consider some algorithms, designed for bigger quantum computers which are not yet developed.
The course material is designed for those computer scientists, engineers and programmers who believe, that there's something else than just HLL programming, that will move our computing power further into infinity.
Since the course is introductory, the only prerequisites are complex numbers and linear algebra. These two are required and they have to be enough.
Happy learning!

Enseigné par

Сысоев Сергей Сергеевич

кандидат физико-математических наук

Transcription

Greetings everyone. Welcome to the course, The Introduction to Quantum Computing prepared for you by the Saint Petersburg State University. My name is Sergey Sysoev and I want to teach all the modulus of this course. So, prepare yourself to see and hear me often during the following five weeks. On this slide, you can see the weeks plan which I call the introduction to introduction. Since the course itself is called The Introduction to Quantum Computing, and theme of this modular is to introduce this course. Let's do it, and the first question is what is this all about? And to answer this question, I'm going to answer first another question. A negative one. I'm going to tell you not what this course is, but what it is not. So, first it is not a course on quantum mechanics. Not at all. All the course material is based on the mathematical model of quantum computing. So, even the basic knowledge in quantum mechanics is not necessary to understand the course material. Second, it is not the software engineering course. The word computing may mislead you. So, here's your warning. We are not going to learn computer languages, programming languages, data structures et cetera. Yes, we are going to design some algorithms. But this course will not probably improve your programming skills in the way you might expect. Now, when we know what we're not going to know, let's see what's left. First, we are going to learn the mathematical model of quantum computing, introduced by the quantum computing pioneer David Deutsch. This model is a very powerful tool for us because it allows us not to dig in the physical nature of quantum computing of a quantum computer, and to design quantum algorithms without even understanding quantum mechanics. We are going to design this mathematical model some quantum algorithms. So, learning objectives are first to understand what these words quantum computing even mean. Why there's so much talk about them these days? Why exactly quantum computer is believed to be so powerful, and is it our future or it's not? I hope to clarify some of these things during this first week. Second, we are going to learn some quantum algorithms, but not just learn them. We are going to understand the principles of their design. So, this is why I write here the design skills. The skills of a quantum computer programmer and quite briefly, we are going to understand that quantum computers are not really the next generation of computing in the common sense. They are not going to substitute the classical computers completely because there are tasks that for which this quantum computers perform the same as classical ones. The prerequisites for this course are linear algebra. You have to understand what it is linear space or some scalar field, what matrices are, what vectors are, how matrix defines an operator, and how to apply this operator to a vector, and what other operations are there in these spaces. The spaces we are going to discuss are field of complex numbers. So they're Hilbert space is not Euclidean. So, different notions of slightly different functions of an angle and a scalar product. And of course to understand why the quantum computer are more powerful than classical, you've got to understand what classical computing is, you have to understand what is an algorithm and what is the complexity of an algorithm et cetera. Learning and understanding is impossible without exercises. So, there are going to be exercises in this course. We'll often have the in-video questions placed there for you to reflect on the new material, and the IQ tests which are slightly more complicated than this in-video questions. And sometimes they're designed not to test your knowledge, but to extended it. And of course, this week there is mandatory for obtaining the course certificate for those who want to. The course is called The Introduction to Quantum Computer which means that there is very much more to learn, and here are some places to start. The most extensive course on the subject to my knowledge is John Preskill's Schools on Quantum Computing available in form of lecture notes on his site of his Internet page in Caltech University. Umesh Vazirani once had a course on Quantum Computing on Coursera. Unfortunately, I don't know what happened to this course but if you would be able to find it, consider yourself very lucky since the course was very good and there are other lectures of Dr Vazirani on the internet and some other topics not from this course. And I also would like to recommend you some popular science books of computer science, be [inaudible] computer science by David Deutch the fabric of reality and the beginning of infinity, and I understand that it's quite uncommon to recommend the popular science books in courses like this. But still I would like to do it, and I believe that these two books can improve your understanding of the subject. And according to this slide, we have just finished the first step. So, let's go further